Redistribution of VCG payments in public project problems

Abstract

Redistribution of VCG payments has been mostly studied in the context of resource allocation. This paper focuses on another fundamental model—the public project problem. In this scenario, the VCG mechanism collects in payments up to n−1n of the total value of the agents. This collected revenue represents a loss of social welfare. Given this, we study how to redistribute most of the VCG revenue back to the agents. Our first result is a bound on the best possible efficiency ratio, which we conjecture to be tight based on numerical simulations. Furthermore, the upper bound is confirmed on the case with 3 agents, for which we derive an optimal redistribution function. For more than 3 agents, we turn to heuristic solutions and propose a new approach to designing redistribution mechanisms.